Perturbative gauge theory at null infinity

TL;DR

This paper develops a boundary theory on null infinity in Minkowski space that captures Yang-Mills radiative modes, reproduces soft gluon theorems via Ward identities, and relates to twistor-string models.

Contribution

It introduces a boundary gauge theory on null infinity that encodes Yang-Mills radiative modes and reproduces known soft theorems through symmetry-based Ward identities.

Findings

Correlation functions produce the full classical Yang-Mills S-matrix.

Ward identities encode leading and subleading soft gluon theorems.

Model suggests a link to twistor-string theories with additional gravitational states.

Abstract

We describe a theory living on the null conformal boundary of four-dimensional Minkowski space, whose states include the radiative modes of Yang-Mills theory. The action of a Kac-Moody symmetry algebra on the correlators of these states leads to a Ward identity for asymptotic 'large' gauge transformations which is equivalent to the soft gluon theorem. The subleading soft gluon behavior is also obtained from a Ward identity for charges acting as vector fields on the sphere of null generators of the boundary. Correlation functions of the Yang-Mills states are shown to produce the full classical S-matrix of Yang-Mills theory. The model contains additional states arising from non-unitary gravitational degrees of freedom, indicating a relationship with the twistor-string of Berkovits & Witten.